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Is this intended to be powered by a single supply? Shouldn’t the motors be powered separately? I assume the power header is used to power both the Arduino and motors, but would powering the Arduino using the barrel-jack work?

The joystick wouldn’t fit into the prototyping are because the holes are too small for the large housing pins, the holes are only 2.54mm apart and the joystick doesn’t conform to standard layout.
Also there isn’t enough space to use another one comfortable on the board.
You could easily use the parts in the Sparkfun eagle library to make your own with two and get it made at BatchPCB
I have been working on a similar venture myself.

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